Methods of and apparatus for inspecting crystals

ABSTRACT

In order to determine the angular orientation of atomic planes in a crystal relative to a reference surface thereof, the crystal is inspected by an X-ray defraction technique in which a pair of X-ray beams are sequentially passed through the crystal from opposite directions while the crystal is rotated through a small arc and monitored for Bragg angle reflections. The two angles at which reflections occur are then averaged to determine an average Bragg angle of reflection. This technique compensates for the situation in which the atomic planes of the crystal are completely oblique to the reference surface by cancelling component vectors of reflection introduced by the complete obliqueness.

[ 51 May 29, 1973 United States Patent 1 Anderson et al.

[54] METHODS OF AND APPARATUS FOR INSPECTING CRYSTALS Primary Examiner-JamesW. Lawrence Assistant Examiner-J3. C. Anderson [75] Inventors: Albin R. Anderson, Lowell; Robert P; Grenier, Newburyport both of Att0rneyW. M. Kdll'l andJ. B. Hoofnagle,.lr. Mass.; Peter R. Perri, Atkinson, N.H.

[57] ABSTRACT In order to determine the angular orientation of [73] Assignee: Western Electric Company, Incorporated, New York, NY. Mar. 1,1972

atomic planes in a crystal relative to a reference sur- 221 Filed:

defraction technique in which a pair of X-ray beams are sequentially passed through the crystal from opposite directions while the crystal is rotated through a small arc and monitored for Bragg angle reflections. The two angles at which reflections occur are then Appl. No.: 230,673

averaged to determine an average Bragg angle of reflection. This technique compensates for the situa- 5 5 131 17] 1 1 W W w w sun; 5 1 1 5 m 0B0 5 5 2H2. "1 W W m h "c -l 8. 0e Us l m C WM .w U.mF .1111 218 555 [.ll

tion in which the atomic planes of the crystal are completely oblique to the reference surface by can- [56] References Cited 3 UNITED STATES PATENTS ceiling component vectors of reflection introduced by the complete obliqueness.

3,448,265 6/1969 Samuelson..........................250/5l 5 3,649,831 3/1972 Eckerlin..............................250/5l5 7 Claims, 6 Drawing Figures Patented May 29, 1973 3 Sheets-Sheet 1 4 ANGULAR DISPLACEMEN PULSE RATE Patented May 29, 1973 3 Sheets-Sheet 2 METHODS OF AND APPARATUS FOR INSPECTING CRYSTALS FIELD OF THE INVENTION The present invention relates generally to the manufacture of piezoelectric quartz crystal elements, and more particularly to automatic apparatus adapted to measure the axial orientation of crystal blanks and to sort the blanks according to the orientation measurements.

BACKGROUND OF THE INVENTION Using piezoelectric quartz crystals in electronic systems is well known. A piezoelectric crystal undergoes a change in dimension or form proportional to an applied electrical potential. Conversely, the crystal generates a surface charge when subjected to stress. The crystal is said to be a piezoelectric resonator when the mechanical resonances of the crystal itself are used to control frequency response.

Crystal blanks for piezoelectric units are cut from quartz stones. When the crystal blank is excited, the resulting modes of motion and the properties of those modes depend markedly on how the surfaces of the cut crystal blanks are oriented relative to the bases of the uncut stones. The angle at which a crystal blank is cut with reference to the natural crystal axis of the uncut stone determines the temperature coefficient of the frequency of the crystal unit. Obviously, to preclude or minimize departures from an assigned frequency as a result of temperature variations, it is essential that this coefficient be as close as possible to zero.

A rectangular uncut quartz stone has a Z or optic axis extending in a longitudinal direction, an X axis extending through one of the apexes of the stone and a Y axis extending normal to both the Z and X axes. The stone is cut along what is generally referred to as the Z-X plane and the angle defined by the Z axis and the resulting crystal face or the Z-Z' angle is especially significant as regards to the temperature coefficient. For AT cuts, the crystal blank is rotated about the X axis and cut along a plane that makes an angle with the Z axis of approximately 35.12". There are of course many other useful crystal cuts involving different angles. This angle can be cut for any particular nominal frequency so that the unit will be stable throughout an extended temperature range, running for example from -5 5 to +90 C.

The Z-Z' crystal angle is highly critical. It is the current practice to cut the Z-Z' angle with diamond saws but the state of this art is not such that it is presently possible to control the angle with sufficient precision so as to produce all blanks within the desired angular specification. On the other hand, the ZZ angle can be chosen for any nominal frequency so thatthe temperature coefficient of frequency is close to zero. Consequently, given broad production requirements for blanks covering the entire frequency spectrum, no blank need be rejected. But since the blanks so cut are different, they must first be individually measured by X-ray diffraction techniques and then sorted into angular increments preparatory to final processing. Blanks from the proper incremental class will thereafter be selected for the fabrication of a group of crystals having a predetermined frequency.

In existing X-ray diffraction techniques for determining the angle between the face of a crystal and its reflected beam as the face of the crystal lies against a reference surface. The angular position of the crystal can then be determined electronically when the detector receives a reflection, thereby establishing the Bragg angle.

PRIOR ART AND TECHNICAL CONSIDERATIONS In one prior art procedure, the X-ray measurement is carried out manually by peaking a signal output meter for maximum reflection and then reading a vernier position indicator mechanically coupled to the turntable to fix the crystal angle. This procedure is of course time-consuming and requires that the turntable be swung slowly in either direction until the peak position is found and the turntable movement arrested to enable a vernier reading to be taken. Thereupon the blank is removed from the turntable and placed into an appropriate grouping. Because of the skill entailed in making the X-ray measurements and the manual operations called uponboth in determining the peak position of the cyrstal blanks and in sorting the blanks, this method does not lend itself to large scale mechanized production. In addition, the manual technique does not ensure the degree of accuracy necessary in current transmission equipment.

In order to increase accuracy and production, automated X-ray equipment has been introduced in which there is provided means for automatically feeding crystal wafer blanks, one at a time, with the X-axis oriented to a Z-axis determining position. At the Z-axis determining position, the crystal wafer blanks are held by a vacuum after being secured in a'reference position to a rotating spindle of the X-ray machine which is automatically rotated through a predetermined angle. During this rotation, a shaft encoder provides an output signal indicating the degree of rotation of the spindle in digital form while X-rays are impinged on the crystal. When Bragg angle reflections from the crystal planes occur, the reflections are detected by a radiation detector, the electrical output of which is amplified and fed to a peak sensing circuit. At the peak of the sensed reflected X-ray's, the peak sensing circuit produces a pulse which is digitally encoded by the shaft encoder, thus indicating digitally the angle of rotation at which the maximum peak occurs. This digital signal from the shaft encoder is used to operate logic circuitry which, in turn, controls a tree type sorter to sort the wafer blanks into one of a large number of bins in accordance with the determined angle of the Z-axis.

These prior art procedures while usually detennining the angular orientation of most crystal planes with adequate accuracy, do not however take into account and compensate for crystal planes which might be skewed in relation to the'reference surface of the crystal. In otherwords, crystals in which the crystal planes make angles with both the Z and X axes of the reference surface of the crystal. Accordingly, a method of and apparatus for discovering and compensating for skewed crystal planes is needed.

SUMMARY OF THE INVENTION It is therefore an object of this invention to provide new and improved methods of and apparatus for more accurately determining the angle that the crystal planes of a crystal make with a reference surface of the crystal.

An additional object of this invention is to provide methods of and apparatus for compensating for compo nent vectors introduced into measurements of crystal plane angles due to skewed orientations of the crystal planes relative to a reference surface.

With these and other objects in view, the present invention contemplates supporting a crystal to be measured on a goniometer spindle for oscillation about the X-axis of the crystal while sequentially directing a first X-ray beam through a reference surface of the crystal while the crystal oscillates in a small arc and then directing a second X-ray beam through a surface opposite the reference surface while the spindle again oscillates in a small are. First and second X-ray detectors are positioned adjacent the reference surface and opposite surface, respectively, to detect the angles of rotation at which Bragg angle reflections occur. These angles are then averaged by electronic circuitry to obtain the correct angle that the crystal planes of the crystal make with the reference surface.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an enlarged isometric view of a quartz crystal of the type inspected by the instant invention schematically showing one atomic plane of many within the crystal skewed relative to a reference surface of the crystal and showing X-ray beams impinging upon and being reflected from top and bottom sides of the atomic plane;

FIG. 2 is a view taken alongline 2-2 of FIG. 1 showing the angles that a reflected X-ray beam makes with the top surface of the atomic plane and with the reference surface of the crystal;

FIG. 3 is a view similar to FIG. 2, however, the quartz crystal has been rotated slightly in the clockwise direc tion and an X-ray beam is shown reflecting from the bottom surface of the atomic plane;

FIG. 4 is an isometric view, schematically arranged, of an X-ray machine and sorting device which may be used to practice the instant invention;

FIG. 5 is a block diagram of a circuit which may be used to control the X-ray machine and sorting device of FIG. 2; and

FIG. 6 is a graph plotting the intensity of two X-ray reflections from a crystal as function of the angle of incidence of.X-ray beams with the crystal.

DETAILED DESCRIPTION Referring now to FIGS. l-3, a rectangular quartz crystal, designated generally by the numeral 10, is shown with a single atomic plane 11 disposed therein which, for purposes of illustration, is indicative of all the atomic planes in the crystal each of which is parallel to the illustrated plane 11. In FIG. 1, the atomic plane 11 is shown skewed in relation to a top reference surface 12 of the crystal 10 forming angles -r in the Z'-Y plane and B in the X-Y plane. For purposes of illustration, the extent of obliqueness of the plane 11 relative to the reference surface 12 is exaggerated. Ordinarily, the angle between the atomic plane 11 and reference surface 12 is approximately 3. It should be noted that FIG. 1 depicts a situation where the plane 11 is completely oblique in relation to the surface 12. In other words, the plane 11 makes angles with both the Z and X axes of the surface 12. The purpose of the instant invention is to accurately determine the angle 1.

In FIG. 2 an X-ray beam 14 contained in the Z'-Y plane is shown passing through the reference surface 12 and forming an angle 7 with the atomic plane 11. Assuming y is the Bragg angle, a reflection will occur from the atomic plane 11 at an angle 7'. 'y' differs from 7 because upon being reflected, the beam 14 moves out of the Z'-Y plane due to an angular component 0) introduced into the reflection because of an angle B that the atomic plane 11 makes with the reference surface 12 in the Z-Y plane. The component to may make the angle 7' slightly greater as is the case illustrated or slightly less as would be the case if the angle B opened in the opposite direction.

The X-ray beam 14 also makes an incidence angle 0 and reflection angle 0' with the reference surface 12. The reflection angle 0' differs from the angle of incidence 0 for two reasons. First of all 0' is larger than 0 due to the angle r that the atomic plane 1 1 makes with the reference surface 12 or the Z axis of the crystal 10. Secondly, 0' is affected by the angular component in the same way as 'y' is affected in that the angle of the atomic plane 12 causes the X-ray beam 14 to bend out of its incidence plane thereby slightly increasing the size of 0' over what it would be if B were zero.

Determining the angle 0' enables one to determine the angle 1 because the Bragg angle for the quartz crystals is known to be 13 20. By simply substracting 13 20 from the angle 0 the angle 1 is obtained. Generally the angle 0 will be approximately 16 20' in which case T will be 3 00. However, it can be readily seen that any error in 0' will result in an error in computing the angle 1'. If the angle B is not zero then there will be an error in the angle 0 because of the angular component w. The prior art methods of and apparatus for de- 7 termining the angle 0' do not compensate for the component a. Consequently, whenever an angle exists, the prior art techniques result in an inaccurate determination of the angle 1.

The present invention compensates for the component m by passing an additional oppositely directed X-ray beam 16 through a surface 17 which is opposite the reference surface 12. As seen in FIG. 3, the beam 16 reflects from the bottom of the atomic plane 11 upon impinging on the atomic plane at an angle equal to the Bragg angle of reflection 7. Due to the angle B, the beam 16 will form an angle 7 upon being reflected from the bottom of plane 11. 'y" is different from y for the same reason that the angle 'y formed by beam 14 is different from 7 upon being reflected from the top of plane 11. The reason of course being that an angular component (0' is introduced into the angle of reflection 7''. However, to is opposite in sign to m and will decrease the size of 'y by the same amount that a) increases the size of 7. Accordingly, an angle 0" between the reflected beam 16 and the reference surface 12 will be decreased by an equivalent amount. Now if 0 is measured and then averaged with 0', then cu and (0 will cancel one another out giving an accurate determination of 1' once the Bragg angle 7 which is a known value is subtracted from the average of 0" and 0.

Referring now to FIG. 4 where there is shown an X-ray machine and sorter for practicing the principles of the invention, the quartz crystal is supported by three nozzles 20 of a vacuum chuck 21 for rotary movement about the X-axis of the crystal. The crystal 10 is initially stored with a plurality of other crystals within a rotary magazine 23. As the magazine 23 indexes in the counterclockwise direction, a carriage 26 which reciprocates on a pair of guide rods 27 engages one of the crystals 10 with a pair of push rods 24 and advances the crystal onto an aligning platform 28 which is spring-supported. The aligning platform 28 has a slot 29 in the top thereof which closely approximates the configuration of the crystals 10 to ensure that each crystal is identically aligned with the nozzles 20. After receiving one of the crystals 10, the aligning platform 28 is advanced upwardly by a vertical transport 31, which spring supports the aligning platform, to engage the crystal with the vacuum nozzles 20. The vertical transport then lowers away from the crystal 10 leaving the crystal supported by the nozzles 20 and ready for sequential inspection by the X-ray beams 14 and 16 as described in FIG. 1.

The X-ray beam 14 is generated by a first X-ray gun 32 positioned above and to the left of the crystal 10 to direct beam 14 at an angle of approximately 10 19 to the Z' axis of the crystal while the X-ray beam 16 is generated by a gun 33 positioned below and to the right of the crystal-to direct beam 16 at an identical angle. Associated with the pair of guns 32 and 33 are a pair of Geiger Mueller X-ray detector tubes 34 and 36, re-

spectively, which sequentially feed signals into a test set designated generally by the numeral 37 when an X-ray reflection is detected by either tube. Circuitry (not shown) is provided to energize the X-ray gun 32 while the crystal oscillates through an arc of about 10 minutes. The gun 32 is then de-energized and the gun 33 energized while the crystal 10 again oscillates through an arc of about l0 minutes.

The test set 37 also receives signals from a displacement transducer 38 indicative of the angular position of the crystal 10 at which X-ray reflections are occurring. The angular orientation of the crystal 10 is achieved by oscillating a spindle 39 of a goniometer 40 to vary the angular position of the vacuum chuck 21 which is secured to one end of the spindle.

The spindle 39 is mounted within a bearing raceway v 41 and is oscillated by an arm 42 which isrigidly secam 44 by a spring 45. The cam 44 is mounted on a shaft 46 which is rotated in one direction by a motor 47. In the preferred embodiment, the cam 44 has a double-lobed profile so that the follower 43 rises and falls twice for each revolution of the shaft 46. While the follower 43 is being lifted by an advancing high profile of the cam 44, the arm 42 pivots in a counterclockwise direction rotating the spindle 39 in a counterclockwise direction within the raceway 41. While the follower 43 is lowering on a low profile portion of the cam 44, the arm 42 pivots in the clockwise direction rotating the spindle 39 in a clockwise direction within the raceway 41. While the spindle 39 is thus oscillating, the raceway 41 is being constantly rotated in one direction by a sprocket 48 which is driven by the shaft 46 with a belt 49. This insures that the various parts of the raceway 41 wear evenly as the spindle 39 oscillates to change the angular orientation of the crystal 10.

The left end of the arm 42 engages a plunger 51 located within the transducer 38 and reciprocates the plunger against an upward bias of a spring (not shown). The position of the plunger 51 is calibrated to be indicative of the angular displacement of the spindle 39 and is thereby indicative of the angular displacement of the crystal 10. As described hereinafter, the signals from tubes 36 are coordinated with the signals from transducer 38 and averaged to accurately disclose the orien tation of atomic planes 11 with respect to the reference surface 12 of the crystal 10 by observing Bragg angle reflections.

After each crystal 10 is scanned by the X-ray beams 14 and 16 and analized by the test set 37, it is directed into a tree sorter, designated generally by the numeral 55. The tree sorter 55 has a plurality of sorting gates 56 each of which is connected to a separate bin (not shown) by chutes 57. Each sorting gate 56 is assigned a value corresponding to an angular orientation of atomic planes 11 in the crystal 10. When the test set 37 determines that angular orientation, only the sorting gate 56 corresponding thereto will be opened.

Since the transport 31 is positioned beneath the nozzles 20, the tree sorter 55 must be set back from the nozzles. Consequently, a directing gate 58 must be hinged to the tree sorter 55 to swing beneath the nozzles 20 and thecrystal 10 prior to releasing the'crystal in order to channel the crystal into the sorter.

The elements of the test set 37 are more fully disclosed in the block diagram of FIG. 5 where the crystal 10 is shown being monitored by the detector tubes 34 and 36. Connected to the detectors 34 and 36 are converters 61 and 62, respectively, which convert pulses from the tubes 34 and 36 into signal pulses suitable for pulse rate counting. The converters 61 and 62 are both connected to a solid state switch 63 which determines whether the X-ray gun 32 is generating the beam 14 and a signal from detector 34 is being applied to a pulse rate counter 64 or whether the X-ray gun 33 is generating the beam 16 and a signal from the detector 36 is being applied to the pulse rate counter.

The setting of the solid state switch 63 is determined by a cam operated mechanical switch 66 which is closed during only half a revolution of the shaft 46 by a single lobed cam 67 (FIG. 4) mounted on the shaft 46 (FIG. 4). When the switch 66 is closed, the switch 63 transmits pulses from the converter 61 to the pulse rate counter 64 and when the switch 66 is open, the switch 63 transmits pulses from the converter 62 to the pulse rate counter. Since the cam 67 (FIG. 4) is single lobed and the cam 44 (FIG. 4) double lobed, the arm 42 will undergo two oscillations for each condition of the switch 63. The crystal 10 which is oscillated by the arm 42 via the spindle 39 is therefore rotated both clockwise and counterclockwise each time it is scanned by one of the X-ray beams 14 or 16.

The pulse rate counter 64 applies a digital signal indicative of pulses per millisecond to a programmable digital comparitor 69 which is programmed to relay signals from the pulse rate counter to an arithmetic unit 70 when instructed to do so by presets 71 and 72. The presets 71 and 72 are operated selectively by a solid state switch 73 which is controlled by the cam operated mechanical switch 66. When the switch 66 is closed, signals from converter 61 and preset 71 are applied simultaneously to the comparitor 69. When the switch 66 is open, signals from the converter 62 and preset 72 are applied to the comparitor 69.

Referring now to FIG. 6 where pulse rates generated by the X-ray beams 14 and 16 are plotted against angular displacement to form curves 74 and 76, it is seen that the pulse rates rapidly increase as the crystal l approaches a critical angle at which reflectivity is a maximum and then rapidly decline. The presets 71 and 72 are set at a pulse rate intensity of about seventy per cent of the maximum pulse rate intensity expected to occur at the critical angle. Since signals from the detectors 34 and 36 are different due to their different orientations relative to the crystal 10, the presets 71 and 72 will of course be set at different values which is why two presets are used. If the pulse rate intensity of either signal does not reach the preset value, then an output signal from the digital comparitor 69 instructs the X-ray machine of FIG. 2 to reject the crystal under consideration, whereupon the vacuum chuck 21 (FIG. 4) releases the crystal and it is directed by the sorting tree 55 (FIG. 4) into a reject bin (not shown).

Referring now to FIG. 5, if the intensity of the signal from the pulse rate counter 64 exceeds the preset value being impressed on the digital comparitor 69 by either preset 71 or 72, then the comparitor instructs the arithmetic unit 70 to accept angular displacement readings from the displacement transducer 38 for as long as the pulse rate counter continues to exceed the preset value.

The arithmetic unit 70 then computes mean valuesrepresented by vertical lines 78 and 79 (FIG. 4) of the angular displacement readings. If the mean value of the angular displacement is determined while detector 34 is generating pulses as represented by the line 78, then the mean value is temporarily stored. However, if the mean value of the angular displacement is determined while detector 36 is generating pulses as represented by line 79, then the mean value is averaged with the stored mean value 78 to compute a final mean value, represented by the line 80. The final mean value 80 is a very accurate determination of the angular displacement at which Bragg reflections occur in individual crystals 10. As mentioned earlier in the discussion of FIG. 1, when the angles of reflection of the X-ray beams 14 and 16 are averaged, the angular components to and 0) caused by oblique or skewed orientation of the atomic planes ll cancel one another out.

A signal indicative of the true angle of reflection is then transmitted by the arithmetic unit 70 to the X-ray machine of FIG. 4 to open the proper gate 56 in the tree sorter 55. After the proper sorting gate 56 is opened, the directing gate 58 is opened and the vacuum released on the nozzles to drop the crystal 10 onto the directing gate whereupon the crystal is directed into the chute and thereafter into the proper bin. In this manner, crystals 10 having identical or approximately identical axial orientations of their respective atomic planes 11 relative to their reference surfaces 12 in the Z' direction, are separated from an assortment of crystals having various axial orientations.

What is claimed is:

1. In a method of measuring the axial orientation of atomic planes in a crystal relative to a reference surface of the crystal where the atomic planes may be completely oblique relative to the reference surface, comprising the steps of:

rotating the crystal about an axis thereof through an arc,

passing radiant energy through a reference surface of the crystal while the crystal is being rotated,

5 determining the angle of rotation at which radiant energy is reflected through the reference surface of the crystal from the atomic planes,

storing the determined angle,

passing radiant energy through a surface of the crystal opposite the reference surface,

determining the angle of rotation at which radiant energy is reflected through the opposite surface from the atomic planes, and

averaging the angle at which radiant energy is reflected through the opposite surface with the stored angle to compensate for inaccuracies introduced into the measurements because of the complete obliqueness.

2. The method of claim 1 wherein the radiation em- 20 ployed is X-radiation.

3. In a method of determining the axial orientation of atomic planes in a crystal wherein the crystal is rotated through a sector intersected by an X-ray beam which is, in turn, monitored for reflections through one surface of the crystal from the atomic planes to determine the angle at which reflections occur, the improvement comprising the steps of:

again rotating the crystal,

impinging an additional X-ray beam through another surface of the crystal,

monitoring the X-ray beam for reflections from the atomic planes through the other surface to determine the angle at which the reflections occur, and averaging the angles at which reflections occur through both the surfaces to determine the axial orientation of the atomic planes in the crystal.

4. In an apparatus for determining the angle of orientation of atomic planes in a crystal relative to a reference surface of the crystal,

means for sequentially focusing oppositely directed X-ray beams for passage into the crystal,

means for angularly displacing the crystal relative to the X-ray beams,

means for detecting Bragg angle X-ray reflections from the crystal,

means for determining the angular positions of the crystal at which Bragg angle reflections occur from the crystal, and

means for averaging the angular positions at which Bragg angle reflections occur to determine the angle of orientation of the atomic planes in the crystal relative to the reference surface of the crystal.

5. The apparatus of claim 4 further including means responsive to said averaging means for directing the crystal to a selected location after the average angular position has been computed.

.6. An apparatus for determining the angle of orientation of atomic planes relative to an axis of a reference surface of a crystal comprising:

means for passing sequentially a pair of X-ray beams through the crystal from generally opposite directions,

means for oscillating the crystal about the axis while the X-ray beams are impinging thereon,

means for detecting Bragg angle reflections from the crystal while the crystal is oscillating,

means for determining when the reflections reach a predetermined level of intensity,

means for computing the mean of the angles at which reflections occur from the crystal after the reflections reach a predetermined level of intensity, and

- means for averaging the mean angles after the angles are computed to determine the angle which the not reach the predetermined level of intensity. 

1. In a method of measuring the axial orientation of atomic planes in a crystal relative to a reference surface of the crystal where the atomic planes may be completely oblique relative to the reference surface, comprising the steps of: rotating the crystal about an axis thereof through an arc, passing radiant energy through a reference surface of the crystal while the crystal is being rotated, determining the angle of rotation at which radiant energy is reflected through the reference surface of the crystal from the atomic planes, storing the determined angle, passing radiant energy through a surface of the crystal opposite the reference surface, determining the angle of rotation at which radiant energy is reflected through the opposite surface from the atomic planes, and averaging the angle at which radiant energy is reflected through the opposite surface with the stored angle to compensate for inaccuracies introduced into the measurements because of the complete obliqueness.
 2. The method of claim 1 wherein the radiation employed is X-radiation.
 3. In a method of determining the axial orientation of atomic planes in a crystal wherein the crystal is rotated through a sector intersected by an X-ray beam which is, in turn, monitored for reflections through one surface of the crystal from the atomic planes to determine the angle at which reflections occur, the improvement comprising the steps of: again rotating the crystal, impinging an additional X-ray beam through another surface of the crystal, monitoring the X-ray beam for reflections from the atomic planes through the other surface to determine the angle at which the reflections occur, and averaging the angles at which reflections occur through both the surfaces to determine the axial orientation of the atomic planes in the crystal.
 4. In an apparatus for determining the angle of orientation of atomic planes in a crystal relative to a reference surface of the crystal, means for sequentially focusing oppositely directed X-ray beams for passage into the crystal, means for angularly displacing the crystal relative to the X-ray beams, means for detecting Bragg angle X-ray reflections from the crystal, means for determining the angular positions of the Rystal at which Bragg angle reflections occur from the crystal, and means for averaging the angular positions at which Bragg angle reflections occur to determine the angle of orientation of the atomic planes in the crystal relative to the reference surface of the crystal.
 5. The apparatus of claim 4 further including means responsive to said averaging means for directing the crystal to a selected location after the average angular position has been computed.
 6. An apparatus for determining the angle of orientation of atomic planes relative to an axis of a reference surface of a crystal comprising: means for passing sequentially a pair of X-ray beams through the crystal from generally opposite directions, means for oscillating the crystal about the axis while the X-ray beams are impinging thereon, means for detecting Bragg angle reflections from the crystal while the crystal is oscillating, means for determining when the reflections reach a predetermined level of intensity, means for computing the mean of the angles at which reflections occur from the crystal after the reflections reach a predetermined level of intensity, and means for averaging the mean angles after the angles are computed to determine the angle which the atomic planes make with the reference surface of the crystal.
 7. The apparatus of claim 6 further including means for rejecting the crystal if the Bragg angle reflections do not reach the predetermined level of intensity. 